Author Archives: Ian Levy

These and Those

More than any of the league’s other postseason awards, Most Improved Player is a construction of ambiguity. Player evaluation is already such an indefinite art that trying to measure the distance between two unknown benchmarks is alchemy to the greatest degree. In the past, several methods of shorthand have been settled on. The award has often been given to effective role-players who see a big jump in minutes, highlighted by a leap in points per game. It also has found its way into the hands of players who jump a talent tier, earning a first All-Star berth of making some other clearly defined adjustment to the quality component of their basketball identity.

By either method, Paul George has to be considered one of the favorites to win the award this season. Becoming an offensive centerpiece for the Pacers, in the absence of Danny Granger, George’s per game scoring average jumped by 5.3 points on the way to earning his first All-Star appearance. This season he has made some definable improvements, transforming his considerable talent into considerable production. His rebounding has been superb and his individual defense elite. There is no question that he is the central pillar of the Pacers’ future.

However, a closer examination reveals some holes in his Most Improved case. George’s eFG% this season is just 49.1%, roughly the same as Metta World Peace’s, and the lowest of his career. On the whole his scoring has been much less efficient this season, and those extra 5.3 points per game are the product of an extra 5.2 shot attempts per game. The real growth areas in George’s game have been in consistent confidence, patience, aggressiveness and leadership. When it comes to actual growth of offensive skill, I’m not sure were looking at something worth celebrating with an award. For the Pacers he has definitely become the “Most,” I’m just not sure about the “Improved.”

While George’s season has been puffed up and paraded around the internet, it has obscured the incredible actual improvement of his teammate Lance Stephenson. Chances are you’ve seen Stephenson only rarely this season, and possibly never before. Even if you’ve been watching him on a regular basis this season, it’s difficult to capture how far he’s come without watching some video of the full-speed train wreck that was his first two seasons. Before this season Stephenson had played 557 NBA minutes, shooting 36.6% from the field, turning the ball over on 22.4% of his possessions and making just 4 of 35 three-pointers. Those numbers are stomach churning but that don’t even begin to capture how painful it was to watch. Once a night he’d make a play that would take your breath away, only to be follow by five minutes of forced jumpers, charging fouls, behind-the-back passes whipped full steam at his teammates’ ankles, and some of the most intent defensive ball-watching you’ve ever seen.

The most bizarre part of the entire experience was the accompanying surplus of barking bravado and chest-pounding confidence. You may remember Stephenson from last year’s playoff series against the Heat, where he barely saw the floor but felt comfortable enough to walk towards the Heat bench during a timeout, making the choke sign. In retrospect, all of that buffoonery was clearly a defense mechanism, a drastic overcompensation. For the first time in his life Stephenson couldn’t just rely on his basketball skills to prove he belonged, and his personality swelled to convince himself, above all others, that he was truly an NBA player.

This season his play on the court is making that statement. He’s chopped nearly a third off his TO%, all the way down to a respectable 14.1%. He’s shooting 45.8% from the field and has made 62 of 187 three-pointers. He attacks the glass ferociously, frequently turning a defensive rebound into a one-man fast break. He makes smart off-the-ball cuts and knows where to find space in the defense for open jumpshots. His individual defense has been physical, challenging, and borderline terrific. The ball-watching breakdowns that were so common in his first two seasons have all but disappeared. His ability to get into the lane and create shots for himself and teammates continues to be nourishment for the offense-starved Pacers. What amazes more than anything, is that all of these developments happened at the same time. This isn’t a case of a role player carving out a niche by discovering how to deploy their one elite skill. Stephenson has become a full-fledged and entirely well-rounded NBA starter.

Last season the Pacers’ starting lineup at the end of the season was a juggernaut. George Hill – Paul George – Danny Granger – David West – Roy Hibbert were leaned on hard by Frank Vogel and they produced at tremendous levels. They outscored the opposition by an average of 14.1 points per 100 possessions, including a +20.2 mark in their six playoff games against the Heat. Granger’s injuries presented a huge hole at the beginning of the season but that same group, with Stephenson in Granger’s place, has outscored opponents by 12.1 points per 100 possessions this year. The only lineup in the league which has played at least 600 minutes and posted a better Net Rating this year is the Thunder’s starting five.

Paul George may have become the face of the franchise, but Lance Stephenson has become the barking, snarling glue that holds them together at both ends of the floor. The Pacers’ identity is painted with broad strokes of bulldog physicality and noone on the roster personifies that better than Stephenson. Paul George climbed a step this season, a difficult step and one which not many players arrive at. But below him on the pyramid Lance Stephenson is leaping steps two-at-a-time.

An Average Perception

I spend a significant chunk of every day fighting to keep up with the stream of splendid basketball writing pouring into my Google Reader. The tide of quality has risen as high as I’ve ever seen it, but the sheer volume means plenty of insight and cleverly constructed prose sinks to the bottom. One ship which has managed to stay afloat in my mind, for almost two weeks now, is Zach Lowe’s piece on the Raptor’s analytic team and their use of data from the SportsVU camera system. The piece is thick with insights to wrestle with, but one piece in particular has continued to stand out.

For Rucker and his team, this is a question that gets at the value of particular shots, the impact of the shot clock, and how coaches teach players. “When you ask coaches what’s better between a 28 percent 3-point shot and a 42 percent midrange shot, they’ll say the 42 percent shot,” Rucker says. “And that’s objectively false. It’s wrong. If LeBron James just jacked a 3 on every single possession, that’d be an exceptionally good offense. That’s a conversation we’ve had with our coaching staff, and let’s just say they don’t support that approach.”

The coaches aren’t even close to being onboard with such a 3-happy philosophy yet. “To have guys who shoot 3s that can’t break that 35 percent break-even point, you have to really evaluate that,” Sterner says.

“You can shoot as many 3s as you’d like,” Casey says, “but if you don’t make them, that philosophy goes out the window. There’s always going to be disagreements. Analytics might give you a number, but you can’t live by that number.”

Casey is obviously right that DeRozan is a bad 3-point shooter. But the analytics team argues that even sub–35 percent 3-point shooters should jack more 3s, and that coaches should probably spend more time turning below-average 3-point shooters into something close to average ones.

“Player development and coaching are scarce resources,” Rucker says. “You only have so much practice time. At a very basic level, a guy going from 25 percent to 30 percent from 3-point range is far more meaningful than a guy improving from 35 percent to 40 percent from midrange.”

These quotes capture a problem that has been collecting dust in the folds of my gray matter; a problem that I had never taken the time to fully unpack. Average shooting on both two and three-point field goals is easily identifiable numerically, and probably most of us could construct a pretty accurate scale of average field goal percentages without meandering over to Basketball-Reference to verify. The problem is that thinking about two and three-point field goal percentage in terms of averages creates a powerful illusion of equivalency. The fact is that the extra point earned by a three-pointer puts those shots on an entirely different cost-benefit scale than that of a two-pointer.

Take the table below. The first column is a list of two-point field goal percentages. The second row is the corresponding three-point field goal percentage, which would provide the same quantity of points per shot. I’ve taken the liberty of highlighting the league average for both 2PT% and 3PT% in yellow.

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Although we often think of average two and three-point shooting as being comparable, they simply aren’t. An average three-point shooter provides scoring efficiency at a level far superior to that of an average two-point shooter.

Just for reference, I’ve also highlighted some percentages in green and red. The green represents the highest field goal percentage in each category put up by a player with enough attempts to qualify for the league’s leader board. The red represents the lowest. That 27.5 3PT% is the work of Monta Ellis and is a number that strikes me as objectively terrible, and represents an outcome that should be avoided at all cost. However, the equivalent 41.0 2PT% strikes me as something that, while not ideal, may be an offensive scenario teams have to live with. My perception of each scale is skewed tremendously, and I have a feeling that I’m in the majority. The vast majority.

Here’s another way to illustrate this comparison. The table below shows a zoomed in and pared down version of the table above, with example players attached to each percentage. The actual two-point percentage values might seem slightly different than what you’d expect but that’s because they are 2PT% not FG%, eliminating three-point attempts for any of those wings and backcourt players.

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Right across the middle of this chart is where perception and reality begin to really clash. Corey Brewer is routinely lambasted for being such a willing and inaccurate three-point shooter. But while his 3.7 three-point attempts per game generate 1.3 negative blog posts per week, rarely is Joe Johnson criticized for the 9.5 two-point shots he attempts each game, even though they generate essentially the same number of points per shot. In the quotes above, the Raptors are talking about investing player development resources into creating average three-point shooters. This is an incredibly important goal in terms of player evaluation and coaching. But even if that goal is out of reach there is a benefit to be had, because a significant swath of below-average three-point shooters still provide advantageously efficient scoring in the context of comparison to the two-point alternative.

Simply put, teams can survive and thrive with below average three-point shooting because of the inherent value of the extra point. But what Lowe captures in those quotes from the Raptors’ coaching staff and analytics team is that the opposite skewed perception persists, not just affecting how individual players are evaluated but also how actual basketball decisions are being made. For all the advanced understandings that have developed and been implemented about the importance of high-value shot selection and the corner three-pointer, it looks more than probable that the three-point shot is still drastically under-utilized.

For a second, let’s go to the extreme edges of hypothetical. Suppose an NBA team were to shoot absolutely nothing but three-pointers. If they were able to make just 33.3% of those shots, about what the Orlando Magic have shot on three-pointers this season (28th in the league), our hypothetical team would still have an eFG% above the league average. Obviously it would be a tremendous stretch for a team to continue making a third of their shots once an opponent realized they were all coming from behind the arc. But even without pushing all the way to the hypothetical extreme, there is a range of efficiency to be gained by pushing shot selection in the three-point direction.

This realization of skewed perception is there, and has been there waiting to be seized and exploited, since the three-point shot was incorporated into the game. It doesn’t require fancy cameras, or statistical databases to uncover, explain or prove. Teams have dabbled with it in the past, but no franchise has made it a foundational component of their offense, enduring through changes in personnel and the coaching staff. But it feels like the league is on the edge of an enormous shift. As the shrouds of misperception are pulled back and opportunities for increased effectiveness are exposed, we may find that we are watching teams, players and a game that looks fundamentally different.

Hunting The Elusive Combo Guard

At this point it’s pretty much accepted that the five traditional basketball positions are, at best, an archaic, generalized umbrella that does a spotty job of capturing the relative skills and responsibilities of players on a basketball court. If you’re still not on board with that statement, I’ll just point out that Dirk Nowitzki and Reggie Evans are both listed as power forwards and leave you to ponder. Despite their shortcomings, these labels continue to be used for several reasons. The first is that they present a common language that almost all basketball fans have grown up with. Even if you are aware of the holes, point guard, shooting guard, small forward, power forward and center give you a way to describe the rest of the cheese in a way that’s almost certain to be understood. The second reason these labels persist is that no comprehensive, viable alternative has been created.

To try and capture the level of detail lacking with the traditional positions, basketball fans and analysts have resorted to using a slew of in-betweens labels, often combining references to the traditional positions with mention of specific skills. This is where we find titles like “stretch-four,” “three-and-D wing,” “point-forward,” “passing center” and “combo guard.” However, I’m not sure that the level of detail captured by these monikers is far superior, still relying on traditional positions for the foundation and taking a very narrow view in modification. Today I want to focus on combo guards, mostly because that particular positional label drives me crazy. It’s also unique in that it doesn’t mention a specific skill but implies the combination of skills sets from two traditional positions – point guards and shooting guards.

In theory, labeling a player as a combo guard is implying that they have the capabilities of filling either traditional backcourt role – operating as a primary facilitator or a primary scorer. In practice, I’ve found that combo guard is usually a sticker slapped onto a shorter player with a deep-seated predilection for shooting the basketball. If we are going to identify combo guards as a real actual basketball creature, a Dr. Moreau hybrid of shooting and passing, we’ll need to differentiate the two positions from which they are supposedly combined.

I began by looking at positional average numbers from Hoopdata. The thing is, differences were hard to find. This season, NBA point guards as a group average 14.5 points per 40 minutes, shooting guards average 15.3. They take nearly an identical number of shots per 40 minutes, 13.2 to 13.7. The same goes for free throws, 3.0 to 3.2. Their shooting percentages are nearly identical as are the actual distribution of their shots from different locations. In fact the only significant difference that I could find was assists – 6.4 per 40 minutes for points guards to 3.3 per 40 minutes for shooting guards. That means that if we’re going to lend some sort of weight to these traditional designations and differentiate between the two, assists have to be the deciding factor. I decided to cut one additional layer and look at the ratios of assists to field goal attempts. My thinking is that if I put the Ast/FGA of every guard onto a continuum, I should be able to identify these elusive combo guards.

What I did was create a Tableau visualization doing exactly that. Each NBA guard who has played at least 700 minutes this season is shown below, graphed by their Ast/FGA. The blue marks are players labelled as point guards on their ESPN player pages. The red marks are those labelled shooting guards. The size of each mark is determined by the player’s assists + field goal attempts per 36 minutes, to give an idea of their overall offensive involvement.

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The keys to our search for combo guards are the colored bands. At the center of the blue and red bands are vertical black lines representing the average Ast/FGA for point guards and shooting guards. The red band stretches to include all players at least one standard deviation above and below the average for shooting guards. The blue band stretches to include all players at least one standard deviation above and below average for point guards. The purple band is the overlap and is where we find our combo guards. These are players who are less than one standard deviation from the average for both positions, a group of 20 names:

  • Aaron Brooks
  • Austin Rivers
  • Brandon Knight
  • C.J. Watson
  • Daniel Gibson
  • Dwyane Wade
  • Evan Turner
  • Isaiah Thomas
  • James Harden
  • Jason Terry
  • Jordan Crawford
  • Kyrie Irving
  • Louis Williams
  • Monta Ellis
  • Norris Cole
  • O.J. Mayo
  • Ramon Sessions
  • Rodney Stuckey
  • Toney Douglas
  • Tyreke Evans

Of those 20 names, 11 are labelled by ESPN as shooting guards, 9 as point guards. They all fit into the, hopefully, more scientific definition of combo guard that I created but are as different as they are similar. Some, like Irving, Wade and Harden are primary offensive focal points for their teams, working in systems that are largely built around their special talents. For some of these players assists are a supplement to their scoring, a response to stout defense walling them off from the basket. For others, scoring is a supplement to their passing, a way to keep the defense off balance. The point is that although these players all have similar ratios of assists to field goal attempts, those ratios are created in very different ways.

We can also use this visualization to identify some players who, although they don’t fit into our combo guard definition, are probably miscast by the traditional labels. J.J. Redick, Lance Stephenson, John Salmons, Kirk Hinrich, Manu Ginobili and Andre Iguodala are all labelled as shooting guards but have Ast/FGA ratios that place them in point guard territory. On the other side of that coin, Shannon Brown, Gary Neal, Randy Foye, Jimmer Fredette and Avery Bradley are all labelled as point guards but have Ast/FGA ratios that put them in shooting guard territory.

Some of those outliers, like Hinrich, Brown and Foye, are clearly there because the traditional labels have simply been misapplied. But others, like Ginobili, Iguodala, and Bradley makes us again examine the purpose and functionality of these positional labels. These players clearly don’t fit into either of the neat boxes that basketball history has so thoughtfully created for us, but they also don’t fit into the new box we cobbled together to try and hold them.

Before I finish, I’ll acknowledge the complete silliness of creating a fancy, interactive graph trying to answer a question that was already asked and answered, by me. The positional labels we use to categorize players, even the psuedo-specific ones we’ve made up ourselves, don’t even begin to capture the actual complex combinations of basketball skills which exist. This is a point you and I were both well aware of before you even started reading. For every player who perfectly fits the bullseye definition of a point guard, combo guard, or point forward, there are four more who exist in the murky space between them. By moving to the label + skill format we’ve made some inroads into embracing complexity, but this is a reminder that there is still a long way to go.

The Dissection of Shot Selection: Historical Trends

Portrait of Young People

Today and tomorrow, I’m one of a legion of representatives from the Truehoop Network at the MIT Sloan Sports Analytics Conference. This incredible two-day event dissects analytics across many sports and many platforms. On the surface this conference is about generating a more complete and detailed understanding of sports, but the theme woven throughout all of the presentations and panels is an eye towards the future. Every sponsor, presenter and attendee is aware that the ideas, products, methods and metrics which are discussed over the next two days have the potential to change the nature of sports forever.

The Sloan Conference and the analytics movement in general can already claim countless victories and advances, from debunking the hot hand, to the introduction of visual-spatial data. In honor of two days spent looking towards the future, I thought I would kick things off with a look at how the dissemination of analytic knowledge has already reshaped the NBA. Over the past few weeks I’ve written a series of posts here at Hardwood Paroxysm about shot-selection using a metric that I created, called Expected Points Per Shot (XPPS). This metric is built on the expected value of shots from different locations and gives us an idea of the quality of a team or player’s shot distribution.

When I started putting together XPPS and XPPS-Allowed numbers for teams, I noticed that clusters of teams from certain seasons appeared around certain averages. The average team XPPS this season is about 1.047, but this is much higher than the average for several of the seasons in my 13 year data sample. When we look closely at those year-by-year averages we can see a very clear trend. The graph below shows the league average XPPS by season, from 2001 to 2013. The overall average, 1.039, is marked by the dashed line.


Although the last six NBA season have seen a series of minor fluctuations, the shot distribution of the average offense changed dramatically and rapidly from 2003 to 2007. To put those numbers in context, the change over that five-year span is roughly equivalent to the difference between the shot-selection of the San Antonio Spurs and the Indiana Pacers this season.

The expected point values for different shots that I use to calculate XPPS are constant since I use averages for the whole 13 season span. For that reason we can rule out increases in efficiency as being responsible for this change. By that I mean that this change is not caused by improvements in league average shooting accuracy over the same period. However, just to make sure we can look at the average FG% from each area of the floor, for each season, over the same time span.

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Again, we see mostly minor fluctuations. There is an interesting downward trend in the FG% of shots from inside the paint (but outside the restricted area). However, at this point it’s difficult to tell if this is something significant or just a fluctuation, slightly larger than expected. The major point is that FG% from each area has been essentially flat over the last thirteen seasons. This means that the overall change in shot-distribution is a product of NBA teams developing a better understanding of what type of shots drive offensive efficiency, and building their offensive systems around this idea.

So what kinds of specific changes have NBA teams been making in their shot distributions? The graph below shows the average percentage of shots that came from each area of the floor, for each season of the past 13 seasons.


Amazingly, it wasn’t until 2007 that shots at the rim made up a bigger portion of the average NBA offense than mid-range jumpers.  Free throws and other shots in the paint have essentially remained flat, and both corner and above the break three-pointers have eaten up the rest the decrease in mid-range jumpers. This graph is fairly simple but it reveals a tremendous shift. The two least efficient areas to shoot from are mid-range and in the paint (not in the restricted area). Over the past 13 seasons, NBA offenses have shaved nearly 10% of their shot attempts from those least efficient areas and moved them to more efficient options. What makes that change even more striking is that being an overall average, it represents the efforts of both offenses and defenses. Teams have used knowledge of efficiency to improve their offense, even while their opponents have been (in theory) using that same knowledge to try and keep them from doing exactly that.

The numbers we just looked at represent the average of all 30 NBA teams across the entire league, lumping together teams who set the pace for these changes with those that are still struggling to implement them. If we look at the team averages over that key 2003 to 2007 time span we can separate out some of those early and late adopters. Here are the top five XPPS marks from that time period:

  1. Memphis Grizzlies – 1.060
  2. Boston Celtics – 1.058
  3. Golden State Warriors – 1.052
  4. San Antonio Spurs – 1.051
  5. Los Angeles Lakers – 1.048

Here are the bottom five:

  1. Minnesota Timberwolves – 1.004
  2. Los Angeles Clippers – 1.022
  3. Dallas Mavericks – 1.027
  4. Toronto Raptors – 1.029
  5. Chicago Bulls – 1.029

It’s interesting that some of the early adopters of statistical analytics are not necessarily the teams who drove this change in shot distribution. It’s possible that teams stumbled onto an efficient style of play, providing a data sample for shrewd organizations to work with, sifting out the benefits. While the early changes may not have been driven purely by analytics, the consistency of the pattern over the past few seasons clearly has been.

This understanding of the relative value of shots has had, and will continue to have, ramifications all over the game of basketball. Knowledge has changed the way the game is played, which alters the way players are trained, evaluated and valued. New positions like the ‘stretch-four’ are now a reality and new systems like the spread pick-and-roll attack of the D’Antoni Suns are now more norm than outlier. Knowledge has reshaped players, coaches, front offices, and the actual manifest interaction of those forces on a basketball court. That kind of knowledge is what brings thousands of fans, professionals, analysts and writers to the MIT Sloan Conference; excited, curious, and hoping for a glimpse of the future.

The Dissection Of Shot Selection: Lessons Learned

ryne: a portrait

Although we usually think of shot selection in the context of offensive decision making, it ‘s really a two-sided coin. Just as teams try to push their own offense into more efficient territory by creating high-quality shots, they can stymie this pursuit of their opponents, choking off efficiency at the other end of the floor. Good defense is not just about forcing misses, it’s also about forcing degree of difficulty. Shot selection has become a much bigger part of the basketball conversation, but again, it mostly focuses on offense. We celebrate teams like the Heat and the Spurs for taking advantage of corner three pointers, but rarely mention teams like the Bulls, that excel at taking those shots away from their opponents. Theoretically, a team that has internalized the importance of shot-selection, and recognizes the full duality of it’s nature, will display evidence of this enlightenment at both ends of the floor.

The shot selection metric I’ve been writing about the past few weeks, Expected Points Per Shot (XPPS), gives us a way of looking at which teams are truly making use of this knowledge. XPPS uses the expected values of shots from different locations to create a single measure, representing the quality of team or player’s shot selection. It also includes free throws, and the lineage of it’s foundational equations can be traced back to TS%. I track both offensive and defensive XPPS numbers at the team level, and looking at the difference between the two reveals those teams for whom shot selection is truly a core value. The table below shows the data for each team this season. For reference, 1.047 XPPS is the league average this season. XPPS is the measure of a team’s offensive shot selection. XPPS Allowed is the measure of a team’s defensive shot selection, or the shot selection they allow their opponents.

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Judging by just XPPS Differential, no team has made more of a focus on shot selection than the Houston Rockets. Their offensive XPPS is 1.102, the highest of any team over the past 13 NBA seasons. They also have an XPPS Allowed of 1.036, way below average and the 8th best mark in the league.  But just looking at this information in numeric form misses some of the nuance. Does the huge XPPS Differential of a team like the Nuggets really come from a focus on both offensive and defensive shot-selection?

The graph below helps bring the full picture into focus. Teams are graphed with their XPPS on the horizontal axis and their XPPS Allowed on the vertical axis. The league average of 1.047 is marked by the dotted lines, dividing the league into four quadrants. The labels of these quadrants (Bad Offense, Good Defense) refer to offensive and defensive shot-selection, not actual offensive and defensive performance. Although I’m sure you’ll see quickly that those things appear to have a strong relationship.

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As you would expect, the league average divides the 30 teams roughly in half when you look at offense and defense separately. However, when we look at them combined we see just five teams (the Spurs, Timberwolves, Rockets, Lakers and Nets) that perform above average in both categories. We can also see that the Nuggets’ XPPS Differential, which was so impressive in numeric format, comes entirely from their performance at the offensive end. It’s incredible that a team so devoted to productive process on offense would be appear to be so thoroughly disinterested in impeding that process for their opponents.

Now there is certainly a difference between intent and the functional results of implementation. It would be unfair, and probably incorrect, to assume that every placement on this graph is the result of a purposeful attention paid to shot selection; or in the opposite, a lack thereof. Still, it’s amazing to me that their isn’t more symmetry to the results here. 18 of the 30 teams in the league have an above average shot selection at one end of the floor, paired with a below average shot selection at the other end.

I also feel strongly that the excuse of talent inadequacies is valid, but only to a certain degree. Saving James Harden and Omer Asik, the Rockets’ roster has no talent in the offensive or defensive extremes. But they are clearly adhering to a system that gives them the best opportunities to maximize their available tools. A team that leans on the excuse of, “we know where we want to shoot from, but aren’t good enough to create those shots” I would point them towards Houston and their passionate fundamentalist devotion to shot selection. Does it feel reasonable to say that the talent on the Rockets’ roster give them a better opportunity to create good shots and limit the same in their opponents, than say the talent of the Celtics or the Warriors?

Three of the best teams in the league this season have been the Heat, Thunder and Clippers. From their placements on this graph they would appear to be entirely unremarkable offensively and defensively. However, we know that to be the exact opposite. Each of those teams is so wealthy with individual talent that they can overcome a lack of extreme efficiency in their systems. Degree of difficulty is nothing to Chris Paul, Kevin Durant and LeBron James. On the other end of the spectrum you find the Spurs, Nets, and again, the Rockets; teams with a decided deficit of individual talent as compared to those other teams. They compensate with an enlightened intent and efficient design. Knowledge and scheme, don’t negate athleticism and natural talent, but they can help level the playing field.

The Dissection Of Shot Selection: Limitations


That faint thumping you hear in the distance, that subtle vibration of the cement and carpet beneath your feet; it’s me once again pounding the drum of shot-selection. Over the past few weeks I’ve brought a few different pieces on the topic here to Hardwood Paroxysm, all built around Expected Points Per Shot (XPPS). If you have not yet been introduced, XPPS is a metric that measures the quality of shot distribution. It is built around the expected values of shots from different locations and rolls the shot-selection of a player or team up into a single number. For context, the league average is 1.047.

XPPS takes its expected values from leagues averages. But because players constantly over and under-perform league averages we also look at Actual Points Per Shot. The difference between the two, is a measure of a player’s shot making ability. Last time we looked at the effect a few different players have on the shot-selection of their teammates. Today I want to share a few shot-selection vignettes, stories of players who have learned specific lessons and are using them to make the most of their offensive opportunities.

‘Can’t Make Them . . . Don’t Take Them’

Michael Kidd-Gilchrist | XPPS 1.093 | Actual Points Per Shot 1.060 | Shot Making Difference -0.033 |

Coming into his rookie season, the biggest question mark in Kidd-Gilchrist’s offensive repertoire was his outside jumpshot. Those concerns have proven to be well-founded as he’s shooting just 25.0% from outside of 8ft. However, Kidd-Gilchrist has demonstrated remarkable restraint and recognition of his own weaknesses – those long-distance shots make up just 28% of his non-turnover offensive possessions. At this point he has posted an XPPS of 1.093, well-above the league average of 1.047. Just 38 players in the league have played at least 750 minutes this season with a shot selection that efficient (XPPS > 1.090). That list of 38 is split fairly evenly between big men and backcourt players or wings. Most of the wings on this list derive their efficiency from a reliance on three-point shots. However, Kidd-Gilchrist is on an island by himself in that just 2.1% of field goal attempts have come from beyond the three-point line. Of all the players on that list of 38, the one his shot selection most closely resembles is Joakim Noah.

In the long-term, a shot distribution of that variety will be an enormous limiting factor. Kidd-Gilchrist’s ability to reach and push through his ceiling will almost certainly be determined by whether or not he can develop a consistent outside shot. At some point moving towards that goal will require him to begin taking and (initially) missing large quantities of jumpshots. But in the meantime it’s refreshing to see a rookie wing, one selected at the top of the NBA Draft, not fall prey to the lure of shot attempts and the pressure to assume offensive leadership. The shots Kidd-Gilchrist is taking this season require much more effort and patience to attain than simply pulling up for a jumper anytime the mood strikes. That a rookie, especially one on a struggling team, would show such a fanatic devotion to playing his role and inhabiting his strengths is truly unique.

‘These Are Better Than Those’

Marcus Morris | XPPS 1.086 | Actual Points Per Shot 1.067 | Shot Making Difference -0.019 |

Last year was an extended struggle for Marcus Morris. He couldn’t crack the Rockets’ front-court rotation and in the 125 minutes he did make it on the floor, Morris forced shots at a prodigious rate. The fact that he took 54 shots in 125 minutes is not quite as unforgivable as the fact that 40 of them came from outside the paint, where he shot just 27.5%. With Omer Asik entrenched in the middle, ability to provide floor spacing from the power forward position is the key to minutes this season and Morris has made some big changes to earn himself a share of those minutes.

First off, Morris is making shots. His Actual Points Per Shot this season has climbed to 1.067, after working out to a basement scraping 0.696 last season. In addition to confidence and repetition, he has made himself a more efficient scorer with a much improved offensive balance. Instead of the nearly 3-to-1 ratio of shots outside and inside the paint he put together as a rookie, Morris now sports a much healthier 1.6-to-1 ratio. Last season, the dreaded mid-range jumpshot constituted 42.6% of his shot attempts. This season it’s been just 15.4% of his arsenal. Morris has also clearly learned some lessons of basic efficiency from his teammate James Harden. Most of those mid-range shots that seem to have disappeared, have really been moved a step or two back, behind the three-point line. Last season, three-pointers accounted for 31.7% of shot attempts, this season it’s been 45.8%.

All of those changes add up to an XPPS of 1.086, well above the league average. His percentage on corner threes is just 29.7% and he’s making just 65.6% of his free throws, accounting for the slightly below-average production as compared to his shot selection. But overall Morris is shooting 37.0% on three-pointers for the season. Consistent rebounding and defense are still concerns, but in terms of understanding his role in the offense and where his shots should be coming from, Morris has come light years from where he was as a rookie.

These Are Even Better Than Those

Quincy Pondexter | XPPS 1.107 | Actual Points Per Shot 1.121 | Shot Making Difference +0.014 |

For the past several years the Memphis Grizzlies have had an incredible offensive advantage on the interior with the frontcourt tandem of Marc Gasol and Zach Randolph. However, that advantage has frequently been strangled by the inability of the Grizzlies’ backcourt to space the floor. Without consistent outside threats, opposing defenses are able to collapse into the lane swarming Randolph and Gasol and rebuffing penetration attempts by Mike Conley and Rudy Gay, all without fear of repercussions. In his 1002 minutes last season, Pondexter was definitely part of the problem. He took almost as many mid-range jumpshots as three-pointers (55 to 71) and finished the year having made just 30.1% of his three-pointers.

This season Pondexter has refined both his shot selection and shot making. His XPPS is up to 1.107 about the same as Shane Battier’s 1.118, and his Actual Points Per Shot is considerably higher than Battier’s 1.080. The biggest improvement has not just been moving mid-range shots out past the three-point line, but also refining his three-point selection. On average, a corner three-pointer is worth 1.157 points per shot, where an above-the-break three-pointer is worth 1.048. If you stretch that out over 100 shots, it’s a difference of 19 points, significant to say the least. Of Pondexter’s 78 three-pointers this season, 62% of them have come from the ultra-efficient corners. On those 48 corner three-pointers, he is shooting 47.9%. Pondexter has been out since the end of December with a sprained knee, and the Grizzlies can’t get him and his floor-spacing back soon enough.

Just Because I Can Make Them, Doesn’t Mean I Should Take Them

Chris Copeland | XPPS 1.075 | Actual Points Per Shot 1.160 | Shot Making Difference +0.085 |

Like Pondexter and Morris, Copeland has fought his way into his team’s rotation with better-than-expected scoring efficiency from the outside. A 28-year old rookie, Copeland has shown a smooth stroke and, through 340 minutes this season, is shooting 45.5% on mid-range jumpers and 38.2% on three-pointers. What makes Copeland so special is that mid-range jumpers make up just 20.8% of his non-turnover offensive possessions, where the league average is 29.6%. By comparison, three-pointers make up 34.6% of Copeland’s non-turnover offensive possessions, where the league averages is 18.1%. That works out to an XPPS of 1.075, well above average, and a mark he is out-performing by an average 0.085 points per shot.

It’s an easy argument that Pondexter, Morris and Kidd-Gilchrist shouldn’t be taking mid-range jumpshots, since they don’t make them very often. But Copeland is a very solid mid-range shooter and still demonstrates a terrific amount of restraint. Even though he’s proven to be a capable mid-range shooter, those shots are still a much less efficient offensive option. This season he has made 15 of 33 mid-range jumpers for an average of 0.909 points per shot. On three-pointers he’s made 21 of 55, for an average of 1.145 points per shot. Even above-average mid-range shooters provide less-efficient scoring on a per-shot basis than average three-point shooters. For a rookie, especially one who may be down to his last chance to carve out a niche in the league, shots are a lifeline. Often we see players in his situation greedily gobble them up in a desperate grab at impact. But Copeland has displayed a razor sharp focus on efficiency and in doing so has probably earned himself an NBA roster spot for as long as his body can sustain him.

All The Marbles

James Harden | XPPS 1.126 | Actual Points Per Shot 1.170 | Shot Making Difference +0.044 |

Everytime I look at these XPPS numbers, I inevitably find myself staring at James Harden. 24 NBA players have played at least 1000 minutes this season with a Usage Rate of more than 25.0%. Of that group, only Kevin Durant and LeBron James have a higher Actual Points Per Shot. None has a higher XPPS.

Durant’s incredibly efficiency is a product of his length, quickness, instincts and that beautifully smooth jumpshot. LeBron’s efficiency is a product of his unique combination of brute strength, transcendent athleticism and understanding of the physical laws of basketball. Harden can claim no similar scaffolding to his offensive performance. His efficiency is not a product of any underlying structure, it is the structure itself. I don’t know if he was gifted with this cloak of efficiency, or if it’s a learned compensation strategy. But the fabric of it is every bit as unique as what LeBron and Durant have.

Just 18.0% of Harden’s shot attempts this season have been mid-range jumpshots. While the league average is 29.6%, average for the group of high-usage scorers to which Harden belongs is actually much higher – 33.1%. Together 72.6% of Harden’s shot attempts come either at the rim or from behind the three-point line and about one out of every five non-turnover offensive possessions he uses results in a trip to the free throw line. Every hesitation dribble, every exploitation of the league’s traveling rules, every step-back three-pointer and every presentation of the ball on a drive to the rim, with an implicit invitation to reach in and foul; these are all real-time examples of Harden pushing pulsing, throbbing life into his skill-set with the fluid of efficiency. If you watch him long enough you can almost see the outer edges of his body dissolve into Matrix-like streams of statistics. Again, I don’t know if James Harden was born a natural scorer, but he certainly plays one on TV.

The Dissection Of Shot Selection: Offensive Gravity


Last week, I used Hardwood Paroxysm to the story of my own personal obsession with shot selection. I’m of the camp that the quality of shots is one of the biggest factors in a team’s offensive success, an opinion I mean to continue codifying and supporting with evidence. My first contribution to this march forward was the development of Expected Points Per Shot (XPPS), a metric for evaluating the quality of a player or team’s shot selection. XPPS is built on the understanding that not all shots are created equal. A layup is much more likely to go in than a long jump shot. A three-pointer is also less likely to go in than a layup, but if it does go in it earns an extra point. All these trade-offs can be measured numerically. I’ve looked at 13 seasons of NBA shot data and calculated the expected value for shots from different areas of the floor. To calculate XPPS, I take a player or team’s shot selection and overlay those expected values to arrive at an average measure of expected points per shot for that player or team.

I have a few disclaimers before we go any further. The first is that XPPS relies on league averages, which means I use the same expected value on a corner three-pointer by Ray Allen as I do for one by Charlie Villanueva. Obviously this lumps everyone together and doesn’t account for a player’s own innate abilities and tendencies. For that reason I usually compare XPPS to Actual Points Per Shot. This helps us see who is over or under-performing the expected value of their shot selection. Second, we are measuring shot selection only by the expected value of each shot’s location. This doesn’t account for defensive proximity or game situation. Although we will be referring to the quality of shots this way in the aggregate, a corner three-pointer well defended and forced at the end of the shot clock is not necessarily a good shot just because it comes from that location. By the same token, mid-range jumpers have the lowest expected value of any shot location, but may actually be a good shot when a wide open opportunity is created within the flow of a well-structured offense. Also, although I use the phrase ‘per shot’ I include shooting fouls and free throws in my calculations, so ‘per scoring opportunity’ may be a better way of thinking about it.

The numbers for both players and teams can be found at Hickory-High. For me these numbers feel like an important first step to some deeper understandings of offensive efficiency. Over the next few weeks here at Hardwood Paroxysm I’m going to be digging into the numbers, trying to parse out trends and some of those important understandings. One of the first things I thought would be interesting to look at in the context of these XPPS numbers, is the way certain players affect the shot selection and shot performance of their teammates.

Nate Silver, of political analytics fame, put together some research in 2011 that found significant added value from a player like Carmelo Anthony in the way his offensive gravity created easier shots for his teammates. Silver’s research found that most of Anthony’s teammates with the Nuggets posted a significantly higher TS% when they played with Anthony as opposed to when they were on the floor without him. Kevin Pelton of Basketball Prospectus did some more digging and found the shooting effect to be slightly smaller than Silver found, but that Anthony also decreased his teammates’ turnover rates quite a bit.

Using XPPS and Actual Points Per Shot we can further this discussion by looking at how the quality of a team’s shot selection and accuracy change with certain players on and off the floor. The first group of players to look at in this context are high-usage scorers, like Anthony. The prevailing wisdom seems to be that having a potent individual scorer, even one who isn’t particularly efficient, puts pressure on the defense, and creates more space for their teammates. To begin testing that idea, I collected the NBA’s top-20 in Usage Rate and calculated their team’s XPPS, Actual Points Per Shot, and Differential when they were on and off the floor. For the ‘on’ portion I subtracted the player’s own points and field goal attempts to focus the results on their teammates. Here is the raw data:

Screen shot 2013-01-10 at 6.59.49 AM

The table above is sorted by the difference in Team XPPS when a player is on the floor, versus when they are off the floor. I find it incredible that the two players in this group who seem to make the biggest difference in the quality of their team’s shot selection are Jamal Crawford and Raymond Felton, both of whom flamed out spectacularly in Portland last season. It is important to remember that these numbers are subject to all the statistical noise one usually finds in On/Off statistics and are heavily influenced by both the other players on the floor and the quality of backups. However, we aren’t using these numbers to judge the overall quality of a player’s production, but rather to look at what they mean to their team. If data tables aren’t your thing, I’ve also created some graphs to show the numbers above.

The chart below shows the On/Off split for each player in XPPS:


Although there definitely seems to be an effect, only a handful of players made a significant difference in the quality of their team’s shot selection. We could probably attribute many of the small differentials to the difference in quality between a starter and a reserve as opposed to a fundamental shift in offensive approach implemented by a specific player. Of course we also need to look at accuracy and the graph below shows each player’s On/Off split for Actual Points Per Shot:


When you look at the graphs, Felton’s importance becomes even more striking. Although he plays most of his minutes with Anthony, his On/Off XPPS split is +0.056, more than twice that of Anthony’s. That may not seem like a huge number, but again we’re looking at things on a per shot basis. Stretched out over 100 shots, the Knicks’ shot selection is nearly six points better with Felton on the floor.

We see the same thing when we look at accuracy, where the Knicks Actual Points Per Shot is +0.098 with Felton on the floor, nearly triple Anthony’s differential. Again, stretching that out over 100 shots that’s a difference of almost 10 points. In an effort to remove as much noise as possible, I also calculated Jason Kidd’s numbers, since he isn’t included in this high-usage group. The Knicks shot selection is slightly worse with Kidd on the floor compared to when he’s off the floor, a mark they are over-performing but not nearly as significantly as the differential for Anthony or Felton.

The Knicks success and overall offensive efficiency have been a huge surprise, at least to me, this season. I wrote in the summer that I was expecting more of the same from them this season, and that I thought Carmelo Anthony’s Olympic summer would actually reinforce his ball-stopping, product-over-process offensive ways. But Anthony is having a career season, especially with regards to his offensive efficiency. His Actual Points Per Shot is up to 1.194 this season, an increase of 0.145 over last season’s 1.049. Most of that bump is because of his three-point shooting. At this point in the season Anthony has made 42.8% of his 6.3 three-point attempts per 36 minutes, both career-highs by a wide margin. It’s possible that at some point in the season his long-range shooting will regress towards his career averages (see Mayo, O.J.), but his overall efficiency won’t drop too far because he has also significantly improved his shot selection this season. Anthony’s XPPS this season is 1.063, up from last season’s 1.045. When we look at his XPPS only when Felton is on the floor, it jumps to 1.072. That means even if Anthony’s shooting averages regress all the way to league averages, he’ll have improved his efficiency by 0.014 points per shot, or 1.4 points per 100 shots, just by improving his shot selection. There are a nearly infinite number of elements here at play, but clearly Felton is doing some positive things for the Knicks’ overall offensive well-being, helping lead the re-focused charge on efficient offensive choices.

One of the other interesting things that I noticed is that several of the players on this list who had a big effect on their team’s shot selection happened to be effective-passing guards and wings – Felton, Crawford, Nate Robinson, Kyrie Irving. Next week we’ll focus on a different group of players, those with high assist rates, and see if we can tease out their effect on the quality of team shot selection.


childerns corner longleat

Long before I discovered basketball analytics, the theme of efficiency was in my blood. In high school, my friends and I used to play midnight pick-up games at an outdoor court behind a nearby elementary school. Basketball may have never been played in a less structured setting, by less talented participants. We would often play 3-on-3, full court, for hours, with neither team threatening to break 30 points. There was no pretense of significance, these games revolved around the simple pleasure of playing basketball with friends.  Still at every pause, I would find myself lecturing my friend Sean about the merits of shot selection. A young man of Pekovic-ian proportions, Sean’s go-to-moves were the step-back-fade-away-three-pointer and the full-court-360-reverse-floater from the free throw line. No one in our circle was even close to matching him physically, but still he chose to approach every possession as if it was a game of HORSE. Even today when I watch Jordan Crawford stumbling over himself to hurl the ball at the rim, I shake my head slowly and think of Sean.

With this strange vein of fun-trampling rationality running through me, I’m delighted to no end by watching shot selection slowly march its way to the center of the basketball discussion. To me there is something fundamentally disturbing about the often incongruous intersections of talent and efficiency. I see the analysis of shot selection as a noble and righteous cause, one that can bring order and beauty to the brutal and chaotic fiefdoms of players like Michael Beasley and Josh Smith.

The central wedge of shot selection’s oozing offensive has been the corner three-pointer. ESPN’s Tom Haberstroh, who recently assumed the PER Diem mantle from John Hollinger, wrote a post earlier this week about the importance of corner three-pointers.

This is a helpful reminder that not all shots are created equal. A corner 3-point shot this season has yielded 1.16 points on average. Your average midrange shot? 0.78 points. That might not seem like a lot on the surface, but it adds up over an entire season.

Generally speaking, exchanging just three midrange shots for three corner 3s per game would yield about 100 additional points over the course of a season. To put some perspective on that, 100 points is roughly equivalent to the difference between the sixth-ranked Miami Heat offense and the 13th-ranked Portland Trail Blazers offense last season (85 points separated them). That is why the midrange game is dying and corner 3s are thriving; shooting 15-foot jumpers is a losing affair compared to other shots.

Not buying the gospel of the corner 3? Believe it or not, a team’s frequency of corner 3s is more closely linked to successful offenses than the frequency of shots in the restricted area, even though they boast similar payoffs (1.16 points per shot versus 1.19 points per shot, respectively). In fact, when we look at shot frequency from the five shot areas on the floor designated by’s StatsCube — restricted-area, in the paint non-restricted-area, midrange, corner 3s and above-the-break 3s — the strongest correlation with offensive efficiency over the past 17 seasons is the corner 3-pointer.

I’ve been working on my own metric for evaluating shot selection – XPPS, or Expected Points Per Shot, and as part of that pursuit I found myself, quite by accident, assembling many of the same numbers that Haberstroh mentioned in his article. Without duplicating his terrific work too emphatically, I want to share directly a few of the numbers I think he was alluding to, and share one other curiosity I discovered.

Using statistics from, I’ve looked at every shot, made and missed, going back to the 2000-2001 season and calculated the average number of points scored by each shot. Looking at three-pointers specifically, I found that over the past 13 seasons a corner three-pointer has averaged 1.157 points. An above-the-break three-pointer has averaged 1.048 points. Obviously each shot scores either three points or no points, but by taking the total number of points scored on those shots and dividing it by the total number of attempts we can evaluate the average accuracy of each shot, expressed in points scored rather than by shooting percentage. Those numbers mean that corner threes score, on average, score 0.109 more points per shot than three-pointers taken above the break. Per 100 attempts, corner threes net nearly 11 more points than their straight-away counterparts.

(The significance will come into play later, but it’s also important to note that, despite coming in at 1.157 points per attempt, corner-threes rank as just the third-most efficient offensive outcome. A shot in the restricted area was worth an average of 1.183 points per attempt over the past 13 seasons. A trip to the free throw line for two shots was worth an average of 1.511 points.) 

Just like Haberstroh, I took those expected point values and measured their connection to overall offensive efficiency. I used the same sample, stretching back to 2001, and looked at the correlation between the percentage of a team’s total field goal attempts that came from each area and that team’s Offensive Rating. Since my XPPS work includes free throw attempts, I included them here as well, using the ratio of free throw attempts to field goal attempts. Haberstroh pointed out that corner threes had the largest correlation, but here are the actual numbers for each:

  • Restricted Area: 0.076
  • In The Paint (Non-RA): -0.184
  • Mid-Range: -0.368
  • Corner Threes: 0.430
  • Above The Break Threes: 0.378
  • Free Throws: 0.174

I then went one step further and calculated correlations between a team’s Offensive Rating and their FG% from each area of the floor. Here are those results:

  • Restricted Area: 0.613
  • In The Paint (Non-RA): 0.464
  • Mid-Range: 0.483
  • Corner Threes: 0.357
  • Above The Break Threes: 0.587
  • Free Throws: 0.265

Surprisingly, accuracy on corner threes has the lowest correlation with Offensive Rating of shots from any area. But take another look, because hidden in those numbers is the statistical equivalent of a flying unicorn:

The correlation between Offensive Rating and the percentage of field goal attempts that were corner threes was 0.430. The correlation between Offensive Rating and FG% on corner-threes was 0.357. That means Offensive Rating is more closely correlated with the percentage of  field goal attempts that are corner threes than it is with their accuracy on those corner threes! 

In his introduction, Haberstroh restates the thesis of enlightened shot-selection fanatics – “Where you take shots is almost as important as whether you make shots.” But incredibly, these numbers, pulled from a suitably large sample size of 13 NBA seasons, imply that in the specific instance of corner threes, where you take shots is MORE important than whether you make shots.

This may be an aberration, the result of some as-yet unexplained statistical noise. There is also some metaphysical element at work here, an effect of the way creating corner threes deforms a defense. Corner-threes are the only offensive outcome where frequency measures out to be more important than accuracy, despite the fact that it is a less valuable outcome on average than shots at the rim, or trips to the free throw line. Further emphasizing their mystical power. But o be clear correlation is not causation, and I’m certainly not trumpeting a call to evaluate offense without the inclusion of accuracy. I ran a few other correlations and the one that had the biggest connection with Offensive Rating was TS%, coming in at a hefty 0.905. Ultimately, making shots still matters more than anything else.

To me the entire dichotomous split between the old standards of basketball analysis and the new set of ever-evolving tools, boils down to a debate between product and process. Measuring teams by their record alone, or players by per-game statistics, is a product-focused view. Measuring teams by their Offensive and Defensive Ratings, and players by per-possession statistics, includes an evaluation of the process by which players and teams arrive at their production.

The single revelation, that for whatever real or imagined reasons, taking more corner threes has been a slightly more common characteristic of efficient offenses than making more corner threes, feels enormous to me. It feels like a monumental brick has been pulled out of the wall defending product-only evaluation, leaving an opening for process to come spilling in. My personal eccentricities my be exaggerating the dimensions of this brick, but I just can’t stop picturing myself fading away behind the three-point line and hurling it at a rusted and ravaged basketball rim.

Moving Towards Efficiency


A very long time ago, I wrote a post at Hickory-High called Reaching for Rhythm. That post was inspired by a Disciples of Clyde discussion, between Bethlehem Shoals and Dan Filowitz, on the perception that Kobe Bryant, LeBron James and several other players had a habit of trying to shoot themselves into a rhythm; in other words beginning the game by taking lots of jumpshots. Shot selection has become a bigger and bigger part of the basketball discussion and thanks to shot location stats from sites like HoopData we’re able to apply numbers to the discussion.

Assigning a numeric value to something can create the illusion of static truth. However, the truth is anything but static. If 35% of a player’s shot attempts have come in the paint, that doesn’t mean their next shot has a 35% chance of coming from inside the paint. Shot selection is the end result of a fluid decision making process. The location of each shot taken is influenced by hundreds of variables – time on the clock, the score, defensive alignment, the player’s energy level, etc. That 35% represents the average of all those different unique situations.

For that ‘Reaching for Rhythm’ post I looked at some of the players who attempted the most shots in the league and tried to identify if they had certain patterns to their shot selection at the beginning of the game compared to the rest of the game. I did this by manually charting the location of their first four shot attempts of each game and then comparing those percentages to their season long averages. At that time LeBron actually had a tendency to attack the rim more at the beginning of games, where Kobe did seem to be taking the “shooting for rhythm route” by taking more long jumpers at the beginning of the game than he did later in the game.

I’ve been wanting to revisit this topic but the idea of manually charting all those shots again was mind numbing. Luckily, in the nearly three years since I wrote that post some new statistical tools have become available and I’ve become a little more proficient at utilizing them. With a little help from the statistical filters at I can isolate a player’s shot selection by quarter. Below are Google Motion graphs the show how the shot selection and efficiency of a handful of players changes of the course of a game. I brought back Kobe and LeBron from the initial discussion and threw in Kevin Durant for the sake of curiosity.

Pressing the play button will start the graph moving. The height of each bar represents the percentage of field goal attempts that came from that area of the floor. The color of each bar represents the eFG% on those shots. Hovering over the bars at any point will give you the actual numbers. For some reason Google automatically reformats the time signature as a year, so 1900 represents the beginning of the game. When the time signature gets to 1912, you’re looking at the player’s numbers for the first quarter, 1924 is the second quarter, etc. One last thing to keep in mind is that the graphs are really only accurate at 12, 24, 36, and 48 minutes; representing the data for the preceding quarter. As the graph moves between each marker it is just moving at a consistent pace to arrive at the next accurate marker.

This data is for games played through 12/7/12.

LeBron has certainly done a lot over the past few seasons to refine his shot selection and maximize efficiency. Over 50% of his first quarter shots this season have come inside the paint. His outside shooting pops up in attempts and down in efficiency in the second and third quarters, but during the fourth quarter it pops back up and he again finds nearly 50% of his shot attempts at the rim. His outside shooting is also much more accurate in the 4th quarter, both on three-pointers and long two-pointers.

Kobe Bryant is much more reliant on the outside shot than LeBron James, but there are elements of an efficient design in his distribution. In every quarter roughly 50% or more of his shot attempts come in the restricted area or from behind the three-point line. I also thought it was amazing to see how much more accurate his three-point shooting became as the game progressed. He does still seem to adhere to the “shooting himself into a rhythm” pattern, as mid-range jumpers make up a greater portion of his shot attempts during the first quarter than at any other point in the game. It’s impressive though that he’s also the most accurate with those shots in the first quarter.

Durant definitely seems to trend towards the shooting himself into a rhythm thread as well – nearly 40% of his shots in the first quarter come from mid-range. From there to the third quarter his mid-range attempts steadily decline while his three-point attempts and shots in the restricted area climb. In the fourth quarter his distribution is fairly consistent but his efficiency is particularly note-worthy – his eFG% is at least 53.0% from every area of the floor.

Although these graphs actually move they still are chasing the moving target of each player’s actual decision making process in attempting shots. They don’t include the variable of time to a degree but still leave plenty of factors to the imagination. But for all they leave out, hopefully they are a reminder that statistics of any stripe are a pared down representation of a menagerie of fact0rs that are constantly in motion.

An Ode To The Wingman

Wingmen: Groom & Best Man

Yesterday, across the state of Minnesota a slew of basketball fans gave thanks for the swift passage of time. It was roughly eight weeks ago that two broken fingers on Kevin Love’s right hand threw a bucket of ice water on the Timberwolves’ plans to step forward and push for a playoff spot. Already dealing with the extended absence of Ricky Rubio, Minnesota was left with a two month storm to weather. Love returned to action on Wednesday night and the Wolves appear to have come through that storm in an incredibly surprising position of strength. As even more injuries piled up during their absence, the fiery collection of role players the Wolves put together this summer to complement Love and Rubio pushed ahead to a 5-4 record, establishing a positive Net Rating and one of the league’s best defenses.

There are 1,001 ways to construct an NBA roster, but every successful iteration relies heavily on a productive and conducive mix of complementary role players. I’m talking about the cutters, the screeners and the defensive glass cleaners. The players who find their shots in the flow of the offense and keep the wheels turning at the defensive end. Those various skills are usually found in clusters, but it’s rare to find a truly versatile cog, one who can complement just about any set of offensive or defensive gears.

Throughout his career Andrei Kirilenko has been one of those cogs. Across 11 seasons and 690 games Kirilenko has put together per game averages of 12.4 points, 5.7 rebounds, 2.8 assists, 1.4 steals and 2.0 blocks. Over that span his team’s offense has been 2.5 points better per 100 possessions with him on the court. At the other end of the floor, his team’s defense has been 3.3 points better per 100 possessions with him on the court. That’s a net difference of +5.8 points per 100 possessions, roughly the difference in overall efficiency between the San Antonio Spurs and the Houston Rockets this season. The only hole in his claim to versatile absolutism is a 31.5 career three-point percentage.

It’s entirely understandable if your perception of Kirilenko is as a slightly more limited player than the numbers above suggest.  He made just over $91 million dollars playing with the Utah Jazz and the roster that was assembled alongside him meant that Kirilenko was often expected to provide more, and in different ways then he was prepared to. When a team asks a supporting cog to be a central piece it’s not always catastrophic, but rarely results in sustainable success. If you remember Kirilenko as a limited, overpaid disappointment it’s understandable. He was probably paid for more than he provided Utah, and he is limited; a fact which disappointed Jazz fans repeatedly. However his limitations were in his ability to take on and succeed with a larger and more central role.

Amazingly though, Kirilenko has been the engine carrying the Timberwolves through this Love-less period. Never quite ready to assume that mantle in Utah, he has assertively placed it on his shoulders this season. But he deserves endless credit for avoiding some of the pitfalls of his Utah time and leading in his own way. Instead of allowing himself to be forced out front and center, Kirilenko has led by continuing to step aside. Instead of stepping forward into a new role for his new team, he sank back into the role he was built for, doing it better than he ever has before.

Other than his a bump in rebounding, his per-game numbers of 14.1 points, 8.3 rebounds, 3.1 assists, 1.4 steals and 2.2 blocks are all roughly equivalent to his career numbers, but that production has come with incredible efficiency. He’s shooting 57.1% from the field and 50.0% on three-pointers. When we look at other efficiency statistics like TS%, eFG%, DRB%, TRB%, AST%, ORtg., and DRtg., we find his production at or near career-highs. One of the only areas where he has seen his number head the other direction is usage. His Usage Rate this season is just 17.0%, nearly a career low.

With the Timberwolves needing an offensive focus Kirilenko has avoided any dangerous desire to fill gaps by using possessions in isolation or pounding the ball in the post. Offensively, everything he’s done has a focus on supporting the overall system. 49.6% of his offensive possessions have come on cuts, spot-ups or in transition. He’s averaging 1.24, 1.70 and 1.34 points per possession in those three offensive situations, shooting a combined 34 of 47. Defensively he’s racked up a total of 33 steals and blocks through nine games. Even more impressive he’s committed just 8 personal fouls, for a ratio of 4.1 defensive plays for each foul.

With huge holes to fill at both ends of the court Kirilenko didn’t try to change his glue-guy nature into some static star-shaped piece. He allowed his versatility to seep in from every angle, filling those holes with oozing efficiency, sealing gaps and holding everything together. My awkward analogies aside, what Kirilenko has done strikes me as indelibly unique. Teams have survived the loss of star player before, but it has almost alway come from the ascension of some new and previously undiscovered star. Kirilenko has not taken this path, he has not made himself a star. He has led his team by simply being the best version of himself.

The Timberwolves now face an entirely new set of challenges, ones of integration and adjustment, moving from an entirely egalitarian ball-movement based attack to one that accommodates the offensive gravity of Kevin Love’s considerable skills. Their Wednesday night loss to the Nuggets in Love’s return demonstrated that this process will take work. But thanks to Andrei Kirilenko that process begins with a winning record and a surprising lack of pressure.